Methods for resistive switching of memristors
The present invention is directed generally to resistive random-access memory (RRAM or ReRAM) devices and systems, as well as methods of employing a thermal resistive model to understand and determine switching of such devices. In particular example, the method includes generating a power-resistance measurement for the memristor device and applying an isothermal model to the power-resistance measurement in order to determine one or more parameters of the device (e.g., filament state).
1. A method for operating a resistive memory device, the method comprising:
providing the device comprising a reactive electrode and an insulator configured to provide a first filament disposed within the insulator, wherein the device is coupled to a monitoring apparatus;
generating a power-resistance measurement for the device by employing the monitoring apparatus; and
applying an isothermal model to the power-resistance measurement in order to determine one or more parameters of the device,
wherein the isothermal model comprises a steady state heat flow model of the filament.
2. The method of claim 1 , wherein the power-resistance measurement is a power-resistance loop.
3. The method of claim 1 , wherein the generating step comprises performing a sweep or series of applied power P app to the device; and monitoring a resistance R of the device during the sweep or series.
4. The method of claim 1 , wherein the generating step comprises performing a sweep or series of applied voltage V app or applied current I app to the device; and monitoring a resistance R or a current I of the device during the sweep or series.
5. The method of claim 4 , wherein the generating step further comprises converting the measured I or R values into the power-resistance measurement.
6. The method of claim 4 , wherein the series of applied voltage V app comprises a series of discrete voltage pulses V pulse.
7. The method of claim 1 , wherein the one or more parameters comprises a filament composition σ, a filament radius r, a surrounding thermal resistance k, a saturation conductivity of the ON state σ max, electrode thermal conductivity k E , a critical activating temperature T crit , a filament temperature, a power threshold, a simulated ON switching curve, and/or a simulated OFF switching curve.
8. The method of claim 7 , wherein the filament composition σ is a conductivity of the filament in the ON state; the filament radius r is a radius of the filament during ON switching and/or OFF switching; and/or the surrounding thermal resistance k is a resistance of the reactive electrode.
9. The method of claim 1 , wherein the steady state heat flow model comprises:
a radial heat flow component characterized by heat flow away from the filament and radially into the insulator surrounding the filament; and
a vertical heat flow component characterized by heat flow away from the filament and through the reactive electrode.
10. The method of claim 9 , wherein the steady state heat flow model comprises:
T
S
=
T
RT
+
σ
V
2
d
E
2
k
E
d
O
[
1
-
k
E
k
F
r
F
2
4
d
E
d
O
]
,
(
Eq
.
1
)
wherein T RT is room temperature, σ is electrical conductivity, V is voltage, d E is electrode thickness, k E is electrode thermal conductivity, d O is thickness of the oxide insulator, r F is filament radius, and k F is filament thermal conductivity.
11. The method of claim 1 , wherein the applying step comprises:
providing the isothermal model for ON switching, which is expressed as:
IV
r
=
A
r
T
crit
-
T
RT
R
-
R
min
,
(
Eq
.
2
a
)
wherein IV r is power dissipation during ON switching, R is resistance during ON switching,
R
min
=
k
E
4
πσ
max
2
L
WF
T
crit
d
E
,
A
r
=
2
k
E
d
O
σ
max
d
E
,
T
RT
is room temperature, σ max is the saturation conductivity of the ON state, V is voltage, d E is electrode thickness, k E is electrode thermal conductivity, d O is thickness of the insulator, r F is filament radius, L WF is the Wiedemann-Franz constant, T crit is critical activating temperature, and k F is filament thermal conductivity; and
determining a fitting value for each of T crit , k E , and σ max as applied to an ON switching curve of the power-resistance loop.
12. The method of claim 11 , wherein the applying step further comprises;
generating a simulated ON switching curve based on Eq. 2a and the fitting values for each of T crit , k E , and σ max .
13. The method of claim 11 , wherein T crit is of from about 1500 K to about 1800 K, k E is of from about 50 W M −1 K −1 to about 300 W M −1 K −1 , and σ max is of from about 6×10 4 Ω −1 m −1 to about 9×10 5 Ω −1 m −1 .
14. The method of claim 1 , wherein the applying step comprises:
providing the isothermal model for OFF switching, which is expressed as:
IV
σ
=
A
σ
T
crit
-
T
RT
R
max
-
R
,
(
Eq
.
2
b
)
wherein IV σ is power dissipation during OFF switching, R is resistance during OFF switching,
R
max
=
4
d
O
2
L
WF
T
crit
d
E
π
r
max
4
k
E
,
A
σ
=
8
d
O
2
L
WF
T
crit
r
max
2
,
r max is the maximum previous filament radius, T RT is room temperature, V is voltage, d E is electrode thickness, k E is electrode thermal conductivity, d O is thickness of the insulator, r F is filament radius, L WF is the Wiedemann-Franz constant, T crit is critical activating temperature, and k F is filament thermal conductivity; and
determining a fitting value for each of T crit , k E , and r max as applied to an OFF switching curve of the power-resistance loop.
15. The method of claim 14 , wherein the applying step further comprises:
generating a simulated OFF switching curve based on Eq. 2b and the fitting values for each of T crit , k E , and r max .
16. The method of claim 14 , wherein T crit is of from about 1500 K to about 1800 K, k E is of from about 50 W M −1 K −1 to about 300 W M −1 K −1 , and r max is of from about 5 nm to about 20 nm.
17. The method of claim 1 , wherein the applying step results in reading an ON state or an OFF state of the first filament.
18. A method for characterizing a resistive memory device, the method comprising:
obtaining a power-resistance measurement for the device, wherein the device comprises a reactive electrode and an insulator configured to provide a first filament disposed within the insulator; and
applying an isothermal model to the power-resistance measurement in order to determine one or more parameters of the device,
wherein the isothermal model comprises a steady state heat flow model of the filament.
19. The method of claim 18 , wherein the applying step comprises employing a set of concentric shells, wherein each shell has a conductivity.